Ginnie Mae has moved slowly with responses to applications, according to David Lykken, an industry consultant.

The U.S.-owned bond insurer has gotten tougher this year about approving lenders even as it’s signed up about 50, Ginnie Mae president Ted Tozer said in a recent interview.

Meanwhile, limited competition in the mortgage space and a lack of capacity to meet demand is helping many lenders—megabanks and nonbanks alike—achieve huge profit margins. (Earlier this month William Dudley, the Federal Reserve Bank of New York president, said mortgage rates are higher than they should be. The Fed plans to acquire $40 billion of home-loan securities a month.)

“More direct access to Fannie would end up in more mortgage companies getting a better price and consumers would benefit,” said John Robbins, head of Bexil American Mortgage Inc., who founded two lenders later sold to banks now part of JPMorgan and Wells Fargo & Co.

“The problem is, if you’re Fannie you just can’t let all these companies have unlimited access. You don’t want to give a high-speed, temperamental race car to someone who just got a driver’s license.”